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X-ray fluorescence analysis of metals in ores and concentrates by Compton scattering
Spectrochimica Acta, Vol. 34B. PP. 177 to I&I Pergamon Press Ltd. 1979. Printed in Great Britain
X-ray fluorescence analysis of metals in ores and concentrates by Compton scattering L. B R O O T H A E R S Metallurgy Department, University of Leuven, de Croylaan 2, 3030 Heverlee, Belgium (Received 21 April 1978; accepted 5 February 1979) Abstract-An X-ray fluorescence method for the analysis of ores and concentrates for one or more metals or other heavy elements is described. A tungsten-target tube is used and the spectral interference of Rayleigh and Compton scattered peaks reduced by a nickel filter. A correlation is established between the. latter peak intensity and the mass absorption coefficient of the sample for the wavelength I .6 A. The values of mass absorption coefficients on both sides of any major element absorption edge are compared and their ratio correlated to the characteristic radiation intensity of that particular element. This permits calculation of mass absorption coefficients across major absorption edges by derivation from the measured p 1.6 value. Spectral interfhences and other difficulties advocate dilution of the samples with dipotassium disulfate. Element concentrations are calculated by comparison with a standard sample and relating mass absorption coefficients and characteristic radiation intensities of both standard and unknown. Precision and accuracy of the method are considered excellent, given the simple nature of the analytical procedure.
1. INTRODUCTION USE of Compton scattering for matrix compensation in the X-ray fluorescence analysis of ores and concentrates has been widely appreciated during recent years, especially in industrial applications. The techniques applied there almost invariably make use of radioisotopic excitation systems that produce high-energy X-rays or low-energy y-rays[ 1,2]. These techniques are generally designed to detect and measure a restricted number of elements only, whereas covered concentration ranges are rather limited and matrices fairly constant. The work illustrated in this paper was carried out at the Mineral Technology Development Centre in Bandung, an institution of the Indonesian Ministry of Mining. This agency is routinely requested to analyse ores of totally different types from all over the territory. The equipment used was a sequential semi-automatic PHILIPS PWl410 fluorescence spectrometer with a tungsten-target tube. The presently outlined method, based on the measurement of Compton scatter, meets with the above mentioned restrictions and offers some practical advantages. Compton scatter was hitherto used in research laboratories mainly in analyses for trace elements in common rocks and soils. This paper describes how this technique can be extended to major element analysis.
T HE
2. THEORY The intensity of Compton scattered X-radiation from an “infinitely thick” sample is directly proportional to the probability of Compton scatter events per unit weight of sample and inversely proportional to the absorption of this radiation by the sample. This statement is valid for a given instrumental geometry and a given primary radiation. The probability that Compton scattering occurs is proportional to the ratio of atomic number 2 over atomic weight A. Hence, it is approximately constant for all elements, only slightly decreasing with increasing atomic number from 0.478 for Na to 0.386 for U. The absorption of X-rays within the sample is predominantly due to the photoelectric effect and varies approximately with Z4/A [2,3]. Hence the Compton scatter intensity from an “infinitely thick” sample is approximately proportional to [I] P. G. B U R K H A L T E R , Anal. C/tern. 43, IO (1971). [2] R. A. FOOKES, V. L. GRAVITIS and J. S. WAN, Anal. Chem. 47, 589 (1975). (31 R. J ENKINS , An Introduction to X-ray Spectrometry. Heyden, New York (1976). 177
178
L.
BR~~THAERS
l/Z’, and will therefore markedly vary with changes in the average atomic number of the sample, decreasing with increasing atomic number of the sample[4]. For a given wavelength of the radiation absorbed by the sample, the mass absorption coefficient i‘s a function of the average atomic number of the sample[31. Generally speaking, the mass absorption coefficient increases with increasing atomic number. However, major discontinuities occur in this trend and are due to the existence of absorption edge phenomena. According to the foregoing considerations, the mass absorption coefficient of a sample for a given wavelength may thus be correlated to the Compton scattered intensity by that sample. This correlation is valid only if no major or minor absorption edge exists between the Compton scattered wavelength and the wavelength for which the mass absorption coefficient is to be measured. REYNOLDS[~] applied this principle to trace element analysis in common rocks. By reducing spectral interferences the same author[6] adapted his method to similar analyses in somewhat heavier samples such as bauxites, laterites and other Fe-oxides. The quite low Compton scatter intensities necessitated the use of a filter to suppress the intensity of the nearby Rayleigh scattered target line peak[6,7]. Element concentrations are calculated with the general formula given by WALKER[~]: c = C Iy cl(AA),, sin 9r+ &AE), sin $2 ” ’ 1, p(AA), sin I+$ + ~(AJS sin $2’ where: C,,, C, Z,, Z, $1. $2 p(AE) p(AA)
are element concentrations (wt%) in unknown and standard sample respectively; are intensities of spectral lines in unknown and standard sample respectively; are the angles made by incident and fluorescent beams respectively, with the sample surface; is the mass absorption coefficient for a given characteristic, secondary, wavelength; is the mass absorption coefficient for the incoming primary radiation.
Equation (1) relates element concentrations and their characteristic radiation intensities in standard and unknown samples to the respective total absorption powers of the same samples. Total absorption includes mass absorption coefficients for both primary and secondary radiations. p(AA) determines the effectiveness with which a characteristic wavelength is excited and therefore varies with the wavelength of that characteristic radiation. It is in practice applicable to replace the continuum of the primary radiation by a hypothetical wavelength which would have the same effect on the excitation of the analysed element. This is the concept of “effective wavelength.” JENKINS[~] states that where only L or M tube lines occur to the short-wavelength .side of the absorption edge of the excited element, the effective wavelength approximately equals 2/3 of the absorption edge wavelength of that element. The application of the effective-wavelength concept provides a means to determine the wavelength for which the primary absorption coefficient w(AA) must be calculated. p(AE) in Equation (1) is known by the correlation between mass absorption coefficient and Compton scatter, on condition that no major or minor absorption edge exists between AE and the Compton scatter wavelength. If this condition is not [4] R. JENKINS and J. L. DE VRIES, Practical X-ray Spectrometry, Macmillan, London (1976). (51 R. C. REYNOLDS, Am. Min. 48, 1133 (1%3). [6] R. C. REYNOLDS , Am. Min. 52, 1493 (1%7). [7] S. E. DE L ONG and D. MCCULLOUGH , Am. Min. 58, 1073 (1973). [8] D. W ALKER , Am. Min. 58, 1069 (1973).
X-ray fluorescence analysis of metals in ores and concentrates by Cowton scattering
179
fulfilled then a mass absorption coefficient must be calculated for a wavelength on the h&side of that particular absorption edge. WALKER@] showed that it is, fortunately, possible to calculate a mass absorption coefficient across an absorption edge. He proved mathematically that the amount of disruption between a mass absorption coefficient on the short-wavelength side, p(AA), and one on the long-wavelength side, p(M), of an absorption edge is proportional to the intensity of the characteristic radiation from the element to which the absorption edge belongs. This author also showed that in practice the ratio p(AA)/p(AE) can best be plotted against the intensity of the characteristic radiation of that particular element. This offers a way to calculate mass absorption coefficients for any wavelength of the spectrum crossing one or more absorption edges. By properly subdividing the spectrum of interest into preselected wavelength intervals, subsequent calculations can extend the mass absorption coefficient measurement to any desired wavelength. All mass absorption’ coefficients are then derived from the mass absorption coefficient for the Compton scatter wavelength. p(AA) can be calculated on the same basis. 3. EXPERIMENTAL The wavelengths of WLa I.2 radiations and their Compton scattered companion peaks are very close to each other: 1.476, 1.487 and 1.500 Angstrom for WLal, WLrr2 and WLalc, respectively (See also Fig. I). The WLrrZc intensity is negligible for the present purposes. For simplicity the symbol WLac then represents WLa Ic. From foregoing considerations follows that the WLac intensity will be low for heavier samples, such as ores and concentrates. Consequently, measurement of WLuc intensity will demand selective reduction of WLcrl,2 intensities. This is accomplished by placing a nickel-filter in front of the scintillation counter. The absorption edge of Ni occurs at A = 1.488 A. The WLaZ-wavelength coincides with the Ni absorption edge so that its intensity will be attenuated to a lesser degree. The Ni-filter was made in the laboratory by mixing NiO powder with a binder and pelletizing it. A filter was obtained with the following properties: Radiation Transmittance %
WLrrc 21
WLa I
wL.o2 14
2
Instrumental conditions were as follows. The tungsten-target tube was operated at 50 kV and 40 mA. The spectrometer was equipped with a LiF200 crystal, a coarse primary collimator (55Opm) and an auxiliary collimator in front of the scintillation detector. 26 - angle u
44
46
I
WLai
400
CuKa
cc 3m
200
im
1hO
Wavelength , A Fig. I. Respective positions of WLa I.2 and other radiations, and Ni-absorption edge.
L. B R O O T H A E R S
180
A fine primary collimator was first tried but did not produce better results. The use of an air path proved satisfactory, though vacuum still increases the WLac intensities by about 25%. Peak counting rates are measured by the fixed count method. An accumulated number of 20,000 counts per measurement proves satisfactory for the purposes of this paper. The Compton scatter intensities are not corrected for background. Major corrections must, however, be made for three possible interfering radiations: NiK& CuKa and
WLa2. (a) NiKp radiation, at A = 1.500 A, coincides with the WLac peak and must consequently be subtracted *from the apparent Compton scatter intensity. A correction procedure is derived from the following. Provided no absorption edge occurs between the two radiations, the intensity ratio Ka/Kp for a given element is constant and is measured. A given filter reduces the intensity of a certain radiation by a characteristic constant factor. It follows then that
f=$.
(2)
where f is a constant, valid only for a given set of instrumental conditions with which the NiKa and KP radiations are measured. The superscripts til and unfil stand for filtered and unfiltered radiations. Measurement of unfiltered NiKa radiation and knowledge of f provide the necessary data to correct the apparent Compton scatter intensity. (b) The angular position of the CuKa radiation peak is very close to the Compton scattered tungsten peak. Overlap with the latter may occur at higher intensities of CuKa. A partial peak overlap correction is much more difficult to make. The problem of CuKa interference can be avoided by reducing characteristic intensities through proper dilution of the samples. (c) The Rayleigh scattered WLa2 peak may overlap the Compton scattered WLac peak. Rayleigh scatter increases with’increasing atomic number. Hence, higher concentrations of heavy elements may produce inconveniently high WLa2 intensities, even with the nickel filter in use. A sufficient dilution of the sample decreases the average atomic number and will eliminate the difficulties. A relationship between the Compton scatter intensity and the mass absorption coefficient for the wavelength 1.6 8, is established. The wavelength 1.6 A was selected knowing that: no K absorption edge occurs between this wavelength and the 1.5 A Compton scatter wavelength; and mass absorption coefficients for the selected wavelength are available from literature. The curve was obtained by plotting the measured Compton scatter intensities against the mass absorption coefficients of a series of known samples (Fig. 2). The samples used consisted of oxides and salts of several elements in finely powdered form. Their mass absorption coefficients were calculated from published data and ranged between the values 30 and 250. The established curve is not linear but displays an excellent correlation. The scatter of the points about it leads to absorption estimation errors of less than 23% relative.
6
Compton scatter . s/2.1$c . Fig. 2. Relation between WLac intensity and mass absorption coefficient for A = 1.6 A. Composition of specimen: 1: SiOl. 2: RzSZO~. 3 : KzSO.+, 4 : CaFr. 5 : Ti02, 6 : Vt05, 7 : Cr20,. 8 : MnOZ, 9: FezOj, IO: AsrO,.
X-ray fluorescence analysis of metals in ores and concentrates by Compton scattering
181
It was found that Compton scatter data from materials heavier than As203 do not fit the curve because of interfering WLa2 radiation. In practice, the intensity ratio IWLol/l~~oc serves well as a means to monitor the interference. This ratio must be smaller than a certain limit value above which WLor2 starts interfering with the Compton peak. The latter limit value is a function of the transmission properties of the utilized filter and, henceforth, an individual characteristic of the experimental set-up. In the present experiments measurement of the intensity ratio on an As,O, specimen sets the limit at 2.8:
The point that represents the data of AszO, appears nearer to the lower end of the Correlation curve because the element as has an absorption edge on the short-wavelength side of the 1.68L reference wavelength. Hence, the mass absorption coefficient of As for A = 1.6 A is low compared to Mn or Fe. Relationships are established between the ratios &iA)/p(AE) and the corresponding characteristic radiation intensities for a few elements of interest. A series of synthetic samples were prepared for that purpose with pure compounds. It was arranged that every element of interest occurs in several samples at different concentration levels. The mass absorption coefficients of these samples, and the subsequent p(AA)/p(AE) ratios, R, were calculated from published data[4]. The R-I curves are valid only for a given set of instrumental conditions with which the characteristic radiation intensities are measured (see Fig. 3). The slopes of these curves are function of several parameters. It must be emphasized that the ratios R are plotted against intensities[S], whilst intensities depend on both concentration and matrix-effect. The curves are not linear but can be considered linear for small concentration- and/or R-ranges. Furthermore, variations of R are smaller for larger differences (AE-AA): see the general outline of a p-A plot. It is pointed out that dilution of the samples is advantageous. Dipotassium disulfate is selected for the present purposes. A dilution of one part of sample to nine parts of K&O, proves satisfactory. K2S207 is a good flux for most metal oxides and sulfides, but a few minerals like cassiterite and zircon and most of the rock-forming silicates remain undissolved.
z ic P.
5OkV
hOmA
1
, -
0
a
I
100
50
CuKa
,
c/s xld
MnKa
.
C/S
x103
2
5ahv
l-4.10
v
40m~
1.35 1
0
50
ZnKa Lo P 0.55 Pl.10 05
,
1
c/s nld
r--=-l
at 0
50
PbLnt
100
Pl.6
50 llv
LO mA
iG 2
1
, c/s a103 0
FeKa
. c/s xrd
Fig. 3. Relations between p(AA)/g(AE) ratios and the characteristic intensities of corresponding elements.
L. BROCITHAERS
182
Dilution restricts sample mass absorption coefficients to a more limited range, within which the or. 1.6-Compton scatter curve can be considered linear.
4. RESULTS , ACCURACY AND PRECISION A priori qualitative knowledge of sample composition indicates how to subdivide the spectrum into appropriate wavelength ranges. For many types of ores and concentrates, the most common major absorption edges are the ones of Mn, Fe, Cu, Zn and Pb. These were, at least, utilized in the frame of the present work. Table 1 lists the wavelengths for which absorption coefficients were computed. Previously selected AE wavelengths are utilized as AA values and substituted to h,e wavelengths in order to simplify calculations. Some authors[9, lo] described methods to correct for background intensities. They established correlations between background count-rates and mass absorption coefficients within one wavelength range. These methods could save the time spent in measuring backgrounds. The estimation of mass absorption coefficients by Compton scatter measurement is one of the error sources. The precision of these measurements was assessed by remeasuring the Compton scatter intensities of a number of samples independently of the first series of measurements. Besides the diluted samples a number of undiluted ones were checked as well. Results are given in Table 2. Standard deviations in this table were calculated as follows: mass absorption coefficients were measured twice on every sample; the differences between duplicate data can be used as a measure of the standard deviations by means of statistical tables (see p. 113 in [ 111). The accuracy of the R-I curves depends basically on the exactitude of the published absorption data[4]. Sequential use of several R-factors in the calculation of a single element concentration expectedly increases errors. The data given in Table 3 on intrasample differences show that the accumulated effect may play a marked role. The “number of R-factors used” refers to the calculation of the secondary absorption coefficients only. The overall precision was evaluated with repeated measurements on a single pellet as well as with single measurements (IT d+IIcate pellets. Yet, figures on intersample differences show clearly that sample preparation Table I. Utilized wavelengths (A) Anal. line
A
&s
AE
TiKrr
2.750
1.66 2.68
MnKa FeKa
2.103 1.937 1.542 1.437 0.982
1.26 1.16 0.92 0.86 0.63
CuKa ZnKa PbLp 1
1.93 1.79 1.60 1.60 1.10
r\A 1.60 1.35 I.10 1.10 I.10 0.55
Table 2. Precision of p-measurements Sample
Undiluted
Diluted
Number of samples Range of fit.6 values Average ~r.~ value Standard deviation Coefficient of variation Errors at 95% conf. levels
8 49.0-80.0 69 1.34 1.94% 3.80%
18 74.0-85.4 80 1.30 1.6% 3.14%
[9] C. E. F EATHER and J. P. WILLIS , X-ray Specrmm. 5, 41 (1976). [lo] J. T. WILBAND, Am. Min. 60. 320 (1975). [l l] M. WINEKATE, Verklarende Statistiek, Spectrum, Utrecht (1974).
0.14 0.74 0.70 I .22 0.69 2.34 2.21 0.71 5.57 5.93
1.61 I.58 0.069 3.18% 0.994
0.14 0.73 0.73 1.27 0.67 2.62 2.15 0.72 5.54 6.98
%Zn Chem* X R F
*Atomic absorption spectrometry. Wolumetry. SColorimetry.
Chem. mean XRF mean Mean abs. error Mean rel. error Carrel. coeff.
0.051 5.66
1.04 2.61
1.03 4.17
Manganese ore Lead cont.
0.05 1 7.17
0.017 2.44
8 0.30-2.20 2
Pb
Sands
Laterites
0.069 0.040 0.240 0.073 0.039 0.055 0.089 0.121 0.104 0.029
0.087 0.086 0.0081 1 I .74% 0.997
0.065 0.025 0.263 0.072 0.036 0.058 0.086 0.130 0.117 0.022
47.86 12.15 30.61 25.69 28.52 31.08 4.81 15.14 22.34 20.47
23.48 23.87 1.202 5.70% 0.992
47.95 13.08 30.08 26.29 26.04 29.07 4.71 16.76 19.52 21.26
9.35 10.53 18.80 19.24 7.42 2.28 3.50 6.07 24.76 17.22 II.91 0.358 3.56% 0.999
I I .75
9.58 10.76 18.33 19.49 7.50 2.08 3.33 6.27 23.80 16.33
10.86 10.75 18.48 24.76 20.70 14.56 19.36 24.64 17.78 20.83 17.85 18.27 0.819 4.07% 0.978
10.89 10.64 18.34 24.22 21.84 14.14 17.93 21.98 18.58 19.91
1.36 2.55 2.98 2.07 3.45 I .77 2.84
2.52 2.43 0. I44 6.2% 0.965
1.32 2.44 3.18 2.04 3.51 2.24 2.94
0.75 I.15 0.44 0.72 0.34 0.36
0.635 0.627 0.02 I 3.96% 0.999
0.78 I.17 0.45 0.73 0.32 0.34
%CLl %Mn %Pb % Fe % TiOz % Ni Chem* X R F Chem* X R F Chem* X R F Chemt X R F Chem$ X R F Chem* X R F
Ore
Table 4. Accuracy Iron
0.013 I .02
0.42 I.48
-
Zinc
7 0.65-2.30 0
5 24-32 I
8 12-31 2
Number of samples Content range (wt%) Number of R-factors used Average intrasample differences* absolute relative (%) Average intersample differencest absolute relative (%)
*Duplicate measurements on single pellets. ISingle measurements on duplicate pellets.
Zn
Fe
Mn
Analysed element
Table 3. Overall precision of the method
184
L. BRO~THAERS
remains a major error source. The overall accuracy of the method is illustrated in Table 4. A number of samples of different ores have been analysed for this purpose. The obtained results are compared with data given by an appropriate chemical method. This accuracy includes errors by both X-ray fluorescence and chemical methods. The results for Cu are somewhat worse as the unexpectedly low countrates increased counting errors. 5. CONCLUSIONS Compton scatter corrections compensate for absorption, both primary and secondary, but not for enhancement. Enhancement effects are however suppressed to a great extent by diluting the samples. It should be possible in specific cases to calculate enhancement factors and treat them as negative absorption coefficients [ 121. Reference to standards provides a correction for long-term drift of the instrument. A great interest lies in the fact that not all elements present in the sample have to be known nor measured. Gangue minerals need not be known at all, which makes previous knowledge of sample composition unnecessary. The use of several R-factors in a calculation sequence may demand measurement of the characteristic radiation of an element of no interest, though not its concentration. The method may be most successfully applied to ores and concentrates as well as to trace elements in rocks and soils. Theoretically, all elements from Na” to U% may be analysed. In practice, there is a lower limit by the fact that every light element necessitates the introduction of another R-factor. The use of a tungsten. target makes it particularly suitable for the transition elements of the fourth period. Acknowledgements--I wish to thank 9. SULASMORO, Director of the Mineral Technology Development Center in Bandung, for the permission to publish this work, as well as the entire staff of this institution, for their cooperation.
[121 M. FRANZINI,
L. LEONI and M. SAIITA, X-ray Spectrom. 5, 208
(1976).
X-ray fluorescence analysis of metals in ores and concentrates by Compton scattering L. B R O O T H A E R S Metallurgy Department, University of Leuven, de Croylaan 2, 3030 Heverlee, Belgium (Received 21 April 1978; accepted 5 February 1979) Abstract-An X-ray fluorescence method for the analysis of ores and concentrates for one or more metals or other heavy elements is described. A tungsten-target tube is used and the spectral interference of Rayleigh and Compton scattered peaks reduced by a nickel filter. A correlation is established between the. latter peak intensity and the mass absorption coefficient of the sample for the wavelength I .6 A. The values of mass absorption coefficients on both sides of any major element absorption edge are compared and their ratio correlated to the characteristic radiation intensity of that particular element. This permits calculation of mass absorption coefficients across major absorption edges by derivation from the measured p 1.6 value. Spectral interfhences and other difficulties advocate dilution of the samples with dipotassium disulfate. Element concentrations are calculated by comparison with a standard sample and relating mass absorption coefficients and characteristic radiation intensities of both standard and unknown. Precision and accuracy of the method are considered excellent, given the simple nature of the analytical procedure.
1. INTRODUCTION USE of Compton scattering for matrix compensation in the X-ray fluorescence analysis of ores and concentrates has been widely appreciated during recent years, especially in industrial applications. The techniques applied there almost invariably make use of radioisotopic excitation systems that produce high-energy X-rays or low-energy y-rays[ 1,2]. These techniques are generally designed to detect and measure a restricted number of elements only, whereas covered concentration ranges are rather limited and matrices fairly constant. The work illustrated in this paper was carried out at the Mineral Technology Development Centre in Bandung, an institution of the Indonesian Ministry of Mining. This agency is routinely requested to analyse ores of totally different types from all over the territory. The equipment used was a sequential semi-automatic PHILIPS PWl410 fluorescence spectrometer with a tungsten-target tube. The presently outlined method, based on the measurement of Compton scatter, meets with the above mentioned restrictions and offers some practical advantages. Compton scatter was hitherto used in research laboratories mainly in analyses for trace elements in common rocks and soils. This paper describes how this technique can be extended to major element analysis.
T HE
2. THEORY The intensity of Compton scattered X-radiation from an “infinitely thick” sample is directly proportional to the probability of Compton scatter events per unit weight of sample and inversely proportional to the absorption of this radiation by the sample. This statement is valid for a given instrumental geometry and a given primary radiation. The probability that Compton scattering occurs is proportional to the ratio of atomic number 2 over atomic weight A. Hence, it is approximately constant for all elements, only slightly decreasing with increasing atomic number from 0.478 for Na to 0.386 for U. The absorption of X-rays within the sample is predominantly due to the photoelectric effect and varies approximately with Z4/A [2,3]. Hence the Compton scatter intensity from an “infinitely thick” sample is approximately proportional to [I] P. G. B U R K H A L T E R , Anal. C/tern. 43, IO (1971). [2] R. A. FOOKES, V. L. GRAVITIS and J. S. WAN, Anal. Chem. 47, 589 (1975). (31 R. J ENKINS , An Introduction to X-ray Spectrometry. Heyden, New York (1976). 177
178
L.
BR~~THAERS
l/Z’, and will therefore markedly vary with changes in the average atomic number of the sample, decreasing with increasing atomic number of the sample[4]. For a given wavelength of the radiation absorbed by the sample, the mass absorption coefficient i‘s a function of the average atomic number of the sample[31. Generally speaking, the mass absorption coefficient increases with increasing atomic number. However, major discontinuities occur in this trend and are due to the existence of absorption edge phenomena. According to the foregoing considerations, the mass absorption coefficient of a sample for a given wavelength may thus be correlated to the Compton scattered intensity by that sample. This correlation is valid only if no major or minor absorption edge exists between the Compton scattered wavelength and the wavelength for which the mass absorption coefficient is to be measured. REYNOLDS[~] applied this principle to trace element analysis in common rocks. By reducing spectral interferences the same author[6] adapted his method to similar analyses in somewhat heavier samples such as bauxites, laterites and other Fe-oxides. The quite low Compton scatter intensities necessitated the use of a filter to suppress the intensity of the nearby Rayleigh scattered target line peak[6,7]. Element concentrations are calculated with the general formula given by WALKER[~]: c = C Iy cl(AA),, sin 9r+ &AE), sin $2 ” ’ 1, p(AA), sin I+$ + ~(AJS sin $2’ where: C,,, C, Z,, Z, $1. $2 p(AE) p(AA)
are element concentrations (wt%) in unknown and standard sample respectively; are intensities of spectral lines in unknown and standard sample respectively; are the angles made by incident and fluorescent beams respectively, with the sample surface; is the mass absorption coefficient for a given characteristic, secondary, wavelength; is the mass absorption coefficient for the incoming primary radiation.
Equation (1) relates element concentrations and their characteristic radiation intensities in standard and unknown samples to the respective total absorption powers of the same samples. Total absorption includes mass absorption coefficients for both primary and secondary radiations. p(AA) determines the effectiveness with which a characteristic wavelength is excited and therefore varies with the wavelength of that characteristic radiation. It is in practice applicable to replace the continuum of the primary radiation by a hypothetical wavelength which would have the same effect on the excitation of the analysed element. This is the concept of “effective wavelength.” JENKINS[~] states that where only L or M tube lines occur to the short-wavelength .side of the absorption edge of the excited element, the effective wavelength approximately equals 2/3 of the absorption edge wavelength of that element. The application of the effective-wavelength concept provides a means to determine the wavelength for which the primary absorption coefficient w(AA) must be calculated. p(AE) in Equation (1) is known by the correlation between mass absorption coefficient and Compton scatter, on condition that no major or minor absorption edge exists between AE and the Compton scatter wavelength. If this condition is not [4] R. JENKINS and J. L. DE VRIES, Practical X-ray Spectrometry, Macmillan, London (1976). (51 R. C. REYNOLDS, Am. Min. 48, 1133 (1%3). [6] R. C. REYNOLDS , Am. Min. 52, 1493 (1%7). [7] S. E. DE L ONG and D. MCCULLOUGH , Am. Min. 58, 1073 (1973). [8] D. W ALKER , Am. Min. 58, 1069 (1973).
X-ray fluorescence analysis of metals in ores and concentrates by Cowton scattering
179
fulfilled then a mass absorption coefficient must be calculated for a wavelength on the h&side of that particular absorption edge. WALKER@] showed that it is, fortunately, possible to calculate a mass absorption coefficient across an absorption edge. He proved mathematically that the amount of disruption between a mass absorption coefficient on the short-wavelength side, p(AA), and one on the long-wavelength side, p(M), of an absorption edge is proportional to the intensity of the characteristic radiation from the element to which the absorption edge belongs. This author also showed that in practice the ratio p(AA)/p(AE) can best be plotted against the intensity of the characteristic radiation of that particular element. This offers a way to calculate mass absorption coefficients for any wavelength of the spectrum crossing one or more absorption edges. By properly subdividing the spectrum of interest into preselected wavelength intervals, subsequent calculations can extend the mass absorption coefficient measurement to any desired wavelength. All mass absorption’ coefficients are then derived from the mass absorption coefficient for the Compton scatter wavelength. p(AA) can be calculated on the same basis. 3. EXPERIMENTAL The wavelengths of WLa I.2 radiations and their Compton scattered companion peaks are very close to each other: 1.476, 1.487 and 1.500 Angstrom for WLal, WLrr2 and WLalc, respectively (See also Fig. I). The WLrrZc intensity is negligible for the present purposes. For simplicity the symbol WLac then represents WLa Ic. From foregoing considerations follows that the WLac intensity will be low for heavier samples, such as ores and concentrates. Consequently, measurement of WLuc intensity will demand selective reduction of WLcrl,2 intensities. This is accomplished by placing a nickel-filter in front of the scintillation counter. The absorption edge of Ni occurs at A = 1.488 A. The WLaZ-wavelength coincides with the Ni absorption edge so that its intensity will be attenuated to a lesser degree. The Ni-filter was made in the laboratory by mixing NiO powder with a binder and pelletizing it. A filter was obtained with the following properties: Radiation Transmittance %
WLrrc 21
WLa I
wL.o2 14
2
Instrumental conditions were as follows. The tungsten-target tube was operated at 50 kV and 40 mA. The spectrometer was equipped with a LiF200 crystal, a coarse primary collimator (55Opm) and an auxiliary collimator in front of the scintillation detector. 26 - angle u
44
46
I
WLai
400
CuKa
cc 3m
200
im
1hO
Wavelength , A Fig. I. Respective positions of WLa I.2 and other radiations, and Ni-absorption edge.
L. B R O O T H A E R S
180
A fine primary collimator was first tried but did not produce better results. The use of an air path proved satisfactory, though vacuum still increases the WLac intensities by about 25%. Peak counting rates are measured by the fixed count method. An accumulated number of 20,000 counts per measurement proves satisfactory for the purposes of this paper. The Compton scatter intensities are not corrected for background. Major corrections must, however, be made for three possible interfering radiations: NiK& CuKa and
WLa2. (a) NiKp radiation, at A = 1.500 A, coincides with the WLac peak and must consequently be subtracted *from the apparent Compton scatter intensity. A correction procedure is derived from the following. Provided no absorption edge occurs between the two radiations, the intensity ratio Ka/Kp for a given element is constant and is measured. A given filter reduces the intensity of a certain radiation by a characteristic constant factor. It follows then that
f=$.
(2)
where f is a constant, valid only for a given set of instrumental conditions with which the NiKa and KP radiations are measured. The superscripts til and unfil stand for filtered and unfiltered radiations. Measurement of unfiltered NiKa radiation and knowledge of f provide the necessary data to correct the apparent Compton scatter intensity. (b) The angular position of the CuKa radiation peak is very close to the Compton scattered tungsten peak. Overlap with the latter may occur at higher intensities of CuKa. A partial peak overlap correction is much more difficult to make. The problem of CuKa interference can be avoided by reducing characteristic intensities through proper dilution of the samples. (c) The Rayleigh scattered WLa2 peak may overlap the Compton scattered WLac peak. Rayleigh scatter increases with’increasing atomic number. Hence, higher concentrations of heavy elements may produce inconveniently high WLa2 intensities, even with the nickel filter in use. A sufficient dilution of the sample decreases the average atomic number and will eliminate the difficulties. A relationship between the Compton scatter intensity and the mass absorption coefficient for the wavelength 1.6 8, is established. The wavelength 1.6 A was selected knowing that: no K absorption edge occurs between this wavelength and the 1.5 A Compton scatter wavelength; and mass absorption coefficients for the selected wavelength are available from literature. The curve was obtained by plotting the measured Compton scatter intensities against the mass absorption coefficients of a series of known samples (Fig. 2). The samples used consisted of oxides and salts of several elements in finely powdered form. Their mass absorption coefficients were calculated from published data and ranged between the values 30 and 250. The established curve is not linear but displays an excellent correlation. The scatter of the points about it leads to absorption estimation errors of less than 23% relative.
6
Compton scatter . s/2.1$c . Fig. 2. Relation between WLac intensity and mass absorption coefficient for A = 1.6 A. Composition of specimen: 1: SiOl. 2: RzSZO~. 3 : KzSO.+, 4 : CaFr. 5 : Ti02, 6 : Vt05, 7 : Cr20,. 8 : MnOZ, 9: FezOj, IO: AsrO,.
X-ray fluorescence analysis of metals in ores and concentrates by Compton scattering
181
It was found that Compton scatter data from materials heavier than As203 do not fit the curve because of interfering WLa2 radiation. In practice, the intensity ratio IWLol/l~~oc serves well as a means to monitor the interference. This ratio must be smaller than a certain limit value above which WLor2 starts interfering with the Compton peak. The latter limit value is a function of the transmission properties of the utilized filter and, henceforth, an individual characteristic of the experimental set-up. In the present experiments measurement of the intensity ratio on an As,O, specimen sets the limit at 2.8:
The point that represents the data of AszO, appears nearer to the lower end of the Correlation curve because the element as has an absorption edge on the short-wavelength side of the 1.68L reference wavelength. Hence, the mass absorption coefficient of As for A = 1.6 A is low compared to Mn or Fe. Relationships are established between the ratios &iA)/p(AE) and the corresponding characteristic radiation intensities for a few elements of interest. A series of synthetic samples were prepared for that purpose with pure compounds. It was arranged that every element of interest occurs in several samples at different concentration levels. The mass absorption coefficients of these samples, and the subsequent p(AA)/p(AE) ratios, R, were calculated from published data[4]. The R-I curves are valid only for a given set of instrumental conditions with which the characteristic radiation intensities are measured (see Fig. 3). The slopes of these curves are function of several parameters. It must be emphasized that the ratios R are plotted against intensities[S], whilst intensities depend on both concentration and matrix-effect. The curves are not linear but can be considered linear for small concentration- and/or R-ranges. Furthermore, variations of R are smaller for larger differences (AE-AA): see the general outline of a p-A plot. It is pointed out that dilution of the samples is advantageous. Dipotassium disulfate is selected for the present purposes. A dilution of one part of sample to nine parts of K&O, proves satisfactory. K2S207 is a good flux for most metal oxides and sulfides, but a few minerals like cassiterite and zircon and most of the rock-forming silicates remain undissolved.
z ic P.
5OkV
hOmA
1
, -
0
a
I
100
50
CuKa
,
c/s xld
MnKa
.
C/S
x103
2
5ahv
l-4.10
v
40m~
1.35 1
0
50
ZnKa Lo P 0.55 Pl.10 05
,
1
c/s nld
r--=-l
at 0
50
PbLnt
100
Pl.6
50 llv
LO mA
iG 2
1
, c/s a103 0
FeKa
. c/s xrd
Fig. 3. Relations between p(AA)/g(AE) ratios and the characteristic intensities of corresponding elements.
L. BROCITHAERS
182
Dilution restricts sample mass absorption coefficients to a more limited range, within which the or. 1.6-Compton scatter curve can be considered linear.
4. RESULTS , ACCURACY AND PRECISION A priori qualitative knowledge of sample composition indicates how to subdivide the spectrum into appropriate wavelength ranges. For many types of ores and concentrates, the most common major absorption edges are the ones of Mn, Fe, Cu, Zn and Pb. These were, at least, utilized in the frame of the present work. Table 1 lists the wavelengths for which absorption coefficients were computed. Previously selected AE wavelengths are utilized as AA values and substituted to h,e wavelengths in order to simplify calculations. Some authors[9, lo] described methods to correct for background intensities. They established correlations between background count-rates and mass absorption coefficients within one wavelength range. These methods could save the time spent in measuring backgrounds. The estimation of mass absorption coefficients by Compton scatter measurement is one of the error sources. The precision of these measurements was assessed by remeasuring the Compton scatter intensities of a number of samples independently of the first series of measurements. Besides the diluted samples a number of undiluted ones were checked as well. Results are given in Table 2. Standard deviations in this table were calculated as follows: mass absorption coefficients were measured twice on every sample; the differences between duplicate data can be used as a measure of the standard deviations by means of statistical tables (see p. 113 in [ 111). The accuracy of the R-I curves depends basically on the exactitude of the published absorption data[4]. Sequential use of several R-factors in the calculation of a single element concentration expectedly increases errors. The data given in Table 3 on intrasample differences show that the accumulated effect may play a marked role. The “number of R-factors used” refers to the calculation of the secondary absorption coefficients only. The overall precision was evaluated with repeated measurements on a single pellet as well as with single measurements (IT d+IIcate pellets. Yet, figures on intersample differences show clearly that sample preparation Table I. Utilized wavelengths (A) Anal. line
A
&s
AE
TiKrr
2.750
1.66 2.68
MnKa FeKa
2.103 1.937 1.542 1.437 0.982
1.26 1.16 0.92 0.86 0.63
CuKa ZnKa PbLp 1
1.93 1.79 1.60 1.60 1.10
r\A 1.60 1.35 I.10 1.10 I.10 0.55
Table 2. Precision of p-measurements Sample
Undiluted
Diluted
Number of samples Range of fit.6 values Average ~r.~ value Standard deviation Coefficient of variation Errors at 95% conf. levels
8 49.0-80.0 69 1.34 1.94% 3.80%
18 74.0-85.4 80 1.30 1.6% 3.14%
[9] C. E. F EATHER and J. P. WILLIS , X-ray Specrmm. 5, 41 (1976). [lo] J. T. WILBAND, Am. Min. 60. 320 (1975). [l l] M. WINEKATE, Verklarende Statistiek, Spectrum, Utrecht (1974).
0.14 0.74 0.70 I .22 0.69 2.34 2.21 0.71 5.57 5.93
1.61 I.58 0.069 3.18% 0.994
0.14 0.73 0.73 1.27 0.67 2.62 2.15 0.72 5.54 6.98
%Zn Chem* X R F
*Atomic absorption spectrometry. Wolumetry. SColorimetry.
Chem. mean XRF mean Mean abs. error Mean rel. error Carrel. coeff.
0.051 5.66
1.04 2.61
1.03 4.17
Manganese ore Lead cont.
0.05 1 7.17
0.017 2.44
8 0.30-2.20 2
Pb
Sands
Laterites
0.069 0.040 0.240 0.073 0.039 0.055 0.089 0.121 0.104 0.029
0.087 0.086 0.0081 1 I .74% 0.997
0.065 0.025 0.263 0.072 0.036 0.058 0.086 0.130 0.117 0.022
47.86 12.15 30.61 25.69 28.52 31.08 4.81 15.14 22.34 20.47
23.48 23.87 1.202 5.70% 0.992
47.95 13.08 30.08 26.29 26.04 29.07 4.71 16.76 19.52 21.26
9.35 10.53 18.80 19.24 7.42 2.28 3.50 6.07 24.76 17.22 II.91 0.358 3.56% 0.999
I I .75
9.58 10.76 18.33 19.49 7.50 2.08 3.33 6.27 23.80 16.33
10.86 10.75 18.48 24.76 20.70 14.56 19.36 24.64 17.78 20.83 17.85 18.27 0.819 4.07% 0.978
10.89 10.64 18.34 24.22 21.84 14.14 17.93 21.98 18.58 19.91
1.36 2.55 2.98 2.07 3.45 I .77 2.84
2.52 2.43 0. I44 6.2% 0.965
1.32 2.44 3.18 2.04 3.51 2.24 2.94
0.75 I.15 0.44 0.72 0.34 0.36
0.635 0.627 0.02 I 3.96% 0.999
0.78 I.17 0.45 0.73 0.32 0.34
%CLl %Mn %Pb % Fe % TiOz % Ni Chem* X R F Chem* X R F Chem* X R F Chemt X R F Chem$ X R F Chem* X R F
Ore
Table 4. Accuracy Iron
0.013 I .02
0.42 I.48
-
Zinc
7 0.65-2.30 0
5 24-32 I
8 12-31 2
Number of samples Content range (wt%) Number of R-factors used Average intrasample differences* absolute relative (%) Average intersample differencest absolute relative (%)
*Duplicate measurements on single pellets. ISingle measurements on duplicate pellets.
Zn
Fe
Mn
Analysed element
Table 3. Overall precision of the method
184
L. BRO~THAERS
remains a major error source. The overall accuracy of the method is illustrated in Table 4. A number of samples of different ores have been analysed for this purpose. The obtained results are compared with data given by an appropriate chemical method. This accuracy includes errors by both X-ray fluorescence and chemical methods. The results for Cu are somewhat worse as the unexpectedly low countrates increased counting errors. 5. CONCLUSIONS Compton scatter corrections compensate for absorption, both primary and secondary, but not for enhancement. Enhancement effects are however suppressed to a great extent by diluting the samples. It should be possible in specific cases to calculate enhancement factors and treat them as negative absorption coefficients [ 121. Reference to standards provides a correction for long-term drift of the instrument. A great interest lies in the fact that not all elements present in the sample have to be known nor measured. Gangue minerals need not be known at all, which makes previous knowledge of sample composition unnecessary. The use of several R-factors in a calculation sequence may demand measurement of the characteristic radiation of an element of no interest, though not its concentration. The method may be most successfully applied to ores and concentrates as well as to trace elements in rocks and soils. Theoretically, all elements from Na” to U% may be analysed. In practice, there is a lower limit by the fact that every light element necessitates the introduction of another R-factor. The use of a tungsten. target makes it particularly suitable for the transition elements of the fourth period. Acknowledgements--I wish to thank 9. SULASMORO, Director of the Mineral Technology Development Center in Bandung, for the permission to publish this work, as well as the entire staff of this institution, for their cooperation.
[121 M. FRANZINI,
L. LEONI and M. SAIITA, X-ray Spectrom. 5, 208
(1976).